Electromagnetic Gauge Field Research Articles

Violation of C/CP symmetry induced by a scalar field emerging from a two-brane universe: A gateway to baryogenesis

A model of baryogenesis is introduced where our usual visible Universe is a 3-brane coevolving with a hidden 3-brane in a multidimensional bulk. The visible matter and antimatter sectors are naturally coupled with the hidden matter and antimatter sectors, breaking the C/CP invariance and leading to baryogenesis occurring after the quark-gluon era. The issue of leptogenesis is also discussed. The symmetry breaking spontaneously occurs due to the presence of an extra scalar field supported by the U(1)⊗U(1) gauge group, which extends the conventional electromagnetic gauge field in the two-brane universe. Observational consequences are discussed. Published by the American Physical Society 2024

Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice

QCD matter in strong magnetic field exhibits a rich phase structure. In the presence of an external magnetic field, the chiral Lagrangian for two flavors is accompanied by the Wess-Zumino-Witten (WZW) term containing an anomalous coupling of the neutral pion π0 to the magnetic field via the chiral anomaly. Due to this term, the ground state is inhomogeneous in the form of either chiral soliton lattice (CSL), an array of solitons in the direction of magnetic field, or domain-wall Skyrmion (DWSk) phase in which Skyrmions supported by π3[SU(2)] ≃ ℤ appear inside the solitons as topological lumps supported by π2(S2) ≃ ℤ in the effective worldvolume theory of the soliton. In this paper, we determine the phase boundary between the CSL and DWSk phases beyond the single-soliton approximation, within the leading order of chiral perturbation theory. To this end, we explore a domain-wall Skyrmion chain in multiple soliton configurations. First, we construct the effective theory of the CSL by the moduli approximation, and obtain the ℂP1 model or O(3) model, gauged by a background electromagnetic gauge field, with two kinds of topological terms coming from the WZW term: one is the topological lump charge in 2+1 dimensional worldvolume and the other is a topological term counting the soliton number. Topological lumps in the 2+1 dimensional worldvolume theory are superconducting rings and their sizes are constrained by the flux quantization condition. The negative energy condition of the lumps yields the phase boundary between the CSL and DWSk phases. We find that a large region inside the CSL is occupied by the DWSk phase, and that the CSL remains metastable in the DWSk phase in the vicinity of the phase boundary.

Field theory of higher-order topological crystalline response, generalized global symmetries and elasticity tetrads

I discuss aspects of higher-order topological field theory of crystalline insulators with no other symmetries. I show how the topology and geometry of the crystalline lattice is organized in terms of so-called elasticity tetrads which are ground state degrees of freedom labelling translational lattice topological charges, higher-form conservation laws and responses on sub-dimensional manifolds of the bulk insulator. The quasitopological responses obtained in this way depend on the lattice and its embedding in space, as expected for weak topology. In a topological crystalline insulator, they classify higher-order responses and global symmetries in a transparent fashion in generic dimensions. This hierarchy coincides with the dimensional hierarchy of topological terms, the multipole expansion, and anomaly inflow, related to a mixed number of elasticity tetrads and electromagnetic gauge fields. In the continuum limit of the elasticity tetrads, the semi-classical expansion in momentum space can be used to derive the higher-order or subdimensional topological responses to local U(1) symmetries, such as electromagnetic gauge fields, with explicit formulas for the higher-order quasi-topological invariants in terms of the elasticity tetrads and Green’s functions. The topological responses in arbitrary dimensions are readily generalized to parameter space to allow for e.g. multipole pumping. The simple results further bridge the recently appreciated connections between topological field theory, higher-form symmetries and gauge fields and their relation to fractonic excitations and topological defects with restricted mobility in the elasticity of crystalline insulators.

Exact universal chaos, speed limit, acceleration, Planckian transport coefficient, “collapse” to equilibrium, and other bounds in thermal quantum systems

We introduce “local uncertainty relations” in thermal many body systems. Using these relations, we derive basic bounds. These results include the demonstration of universal non-relativistic speed limits (regardless of interaction range), bounds on acceleration or force/stress, acceleration or material stress rates, transport coefficients (including the diffusion constant and viscosity), electromagnetic or other gauge field strengths, correlation functions of arbitrary spatio-temporal derivatives, Lyapunov exponents, and thermalization times. We further derive analogs of the Ioffe–Regel limit. These bounds are relatively tight when compared to various experimental data. In the ħ→0 limit, all of our bounds either diverge (e.g., the derived speed and acceleration limit) or vanish (as in, e.g., our viscosity and diffusion constant bounds). Our inequalities hold at all temperatures and, as corollaries, imply general power law bounds on response functions at both asymptotically high and low temperatures. Our results shed light on how apparent nearly instantaneous effective “collapse” to energy eigenstates may arise in macroscopic interacting many body quantum systems. We comment on how random off-diagonal matrix elements of local operators (in the eigenbasis of the Hamiltonian) may inhibit their dynamics.

Towards a self-interacting complex scalar field boson-star model

Abstract We propose a simple model intended to address boson stars (BSs) in a theory of self-interacting massive charged scalar fields coupled to the electromagnetic (EM) gauge field and gravity. We first consider standard scalar electrodynamics (SED) in 3 + 1 flat space-time dimensions in which only a complex scalar field and the EM field are present in the Lagrangian of the system. In order to better understand scalar field dynamics in 3 + 1 $\left(3+1\right)$ -dimensions we reduce the space dimensions to 2 and solve a problem consisting of embedded interacting charged scalar particles moving on the polar plane in the presence of certain linear static EM fields. If the 3 + 1 $\left(3+1\right)$ -dimensional system is consistently coupled to gravity, we comment on the possible relevance of this approach to study BS dynamics.

Fractional quantum Hall effect for extended objects: from skyrmionic membranes to dyonic strings

It is well known that in two spatial dimensions the fractional quantum Hall effect (FQHE) deals with point-like anyons that carry fractional electric charge and statistics. Moreover, in presence of a SO(3) order parameter, point-like skyrmions emerge and play a central role in the corresponding quantum Hall ferromagnetic phase. In this work, we show that in six spatial dimensions, the FQHE for extended objects shares very similar features with its two-dimensional counterpart. In the higher-dimensional case, the electromagnetic and hydrodynamical one-form gauge fields are replaced by three-form gauge fields and the usual point-like anyons are replaced by membranes, namely two-dimensional extended objects that can carry fractional charge and statistics. We focus on skyrmionic membranes, which are associated to a SO(5) order parameter and give rise to an higher-dimensional generalizaton of the quantum Hall ferromagnetism. We show that skyrmionic membranes naturally couple to the curved background through a generalized Wen-Zee term and can give us some insights about the chiral conformal field theory on the boundary. We then present a generalization of the Witten effect in six spatial dimensions by showing that one-dimensional extended monopoles (magnetic strings) in the bulk of the FQH states can acquire electric charge through an axion field by becoming dyonic strings.

Dynamical piezomagnetic effect in time-reversal-invariant Weyl semimetals with axionic charge density waves

Charge density waves (CDWs) in Weyl semimetals (WSMs) have been shown to induce an exotic axionic insulating phase in which the sliding mode (phason) of the CDW acts as a dynamical axion field, giving rise to a large positive magnetoconductance [Wang et al., Phys. Rev. B 87, 161107(R) (2013); Roy et al., Phys. Rev. B 92, 125141 (2015); J. Gooth et al., Nature (London) 575, 315 (2019)]. In this work, we predict that dynamical strain can induce a bulk orbital magnetization in time-reversal (TR)-invariant WSMs that are gapped by a CDW. We term this effect the ``dynamical piezomagnetic effect'' (DPME). Unlike in J. Gooth et al. [Nature (London) 575, 315 (2019)], the DPME introduced in this work occurs in a bulk-constant (i.e., static and spatially homogeneous in the bulk) CDW, and does not rely on fluctuations, such as a phason. By studying the low-energy effective theory and a minimal tight-binding (TB) model, we find that the DPME originates from an effective valley axion field that couples the electromagnetic gauge field with a strain-induced pseudogauge field. In particular, whereas the piezoelectric effects studied in previous works are characterized by 2D Berry curvature, the DPME represents the first example of a fundamentally 3D strain effect originating from the Chern-Simons 3-form. We further find that the DPME has a discontinuous change at a critical value of the phase of the CDW order parameter. We demonstrate that, when there is a jump in the DPME, the surface of the system undergoes a topological quantum phase transition (TQPT), while the bulk remains gapped. Hence, the DPME provides a bulk signature of the boundary TQPT in a TR-invariant Weyl CDW.

Bulk plasmaritons: Wave-mechanical and second-quantized theories

Inspired by a recently established quantum theory for bulk and surface plasmons [Jung and Keller, Phys. Rev. A 103, 063501 (2021).], wave-mechanical and second-quantized quantum electrodynamic theories for bulk plasmaritons in a homogeneous jellium are presented. Starting from the ``inner'' structure of the transversely polarized classical plasmariton mode, it is argued that a plasmariton quasiparticle may be formed by an always attached pair consisting of a transverse (gauge) photon and a never observable transverse plasmon. A first-quantized plasmariton theory is established from a plasmariton Klein-Gordon equation. It is shown that the plasmariton can be perceived as a diamagnetically driven spin-1 boson quasiparticle. A Lagrangian-Hamiltonian formalism is used to extend the first-quantized plasmariton theory to the second-quantized level. The minimal coupling principle is used to change the free QED theory into a theory coupling the plasmariton to an electromagnetic gauge field. Using the microscopic transverse Lindhard (random phase approximation) dielectric function, it is shown that for small wave numbers, the classical Boltzmann equation part of the Lindhard dielectric function results in a hydrodynamic Brewster branch, the quantization of which follows that of a vectorial Klein-Gordon equation. For plasmariton wave numbers larger than the Fermi wave number, a pure electrostatic model (with no magnetic-field component) results in a harmonic-oscillator description of the plasmariton's polarization field. With inspiration and elements from the Power-Zinau-Wolley description, the Pauli-Fierz theory for particle-tied transverse photons, and the propagator theory of Keller for the spatial localization of transverse photons, a formalism in which the plasmariton quasiparticle is dressed by a cloud of transverse (long-wavelength) photons is developed. The quantized radiated part of the electromagnetic field is described by a free-field quantization of the transverse part of the displacement field (${\mathbf{D}}_{T}$). The total Hamiltonian is diagonalized, and the resulting dispersion relation obtained. The interaction between the transverse radiated and attached photons implies that a strongly localized and charged plasmariton quasiparticle with its tied photons vibrates as a simple harmonic oscillator in the ``external'' radiative transverse photon field.

Unquantized anomalies in topological semimetals

Topological semimetals are a new class of metallic materials, which exist at band fillings that ordinarily correspond to insulators or compensated accidental semimetals with zero Luttinger volume. Their metallicity is a result of nontrivial topology in momentum space and crystal symmetry, wherein topological charges may be assigned to point band-touching nodes, preventing gap opening, unless protecting crystal symmetries are violated. These topological charges, however, are defined from noninteracting band eigenstates, which raises the possibility that the physics of topological semimetals may be modified qualitatively by electron-electron interactions. Here we ask the following question: what makes the topological semimetals nontrivial beyond band theory? Alternatively, can strong electron-electron interactions open a gap in topological semimetals without breaking the protecting symmetries or introducing topological order? We demonstrate that the answer is generally no, and what prevents it is their topological response, or quantum anomalies. While this is familiar in the case of magnetic Weyl semimetals, where the topological response takes the form of an anomalous Hall effect, analogous responses in other types of topological semimetals are more subtle and involve crystal symmetry as well as electromagnetic gauge fields. Physically these responses are detectable as fractional symmetry charges induced on certain gauge defects. We discuss the cases of type-I Dirac semimetals and time-reversal invariant Weyl semimetals in detail. For type-I Dirac semimetals, we also show that the anomaly vanishes, in a nontrivial manner, if the momenta of the Dirac nodes satisfy certain exceptional conditions.

Bulk and surface plasmons: Wave-mechanical and second-quantized theories

In this paper we formulate the quantum theory for longitudinal (rotational free) collective electron modes, the so-called plasmons. Starting from the jellium dispersion relation, a first-quantized wave-mechanical theory is established. We show that plasmon quantum (quasi)particles are charged bosons described by complex Klein-Gordon fields satisfying a ``relativistic'' scalar Klein-Gordon equation in which the speed of light $c$ is replaced by a velocity $a$ on the order of the Fermi velocity. Based on a formally ($c\ensuremath{\rightarrow}a$) covariant description, the first-quantized theory is extended to the second-quantized level via a Lagrangian formalism. We show how the second-quantized theory enables the study of the plasmon quantum particles interaction with an electromagnetic gauge field via a modification of the free plasmon Lagrangian density by the minimal coupling principle. Utilizing the Weyl expansion, first- and second-quantized theories for surface-plasmon quantum particles are established in close analogy to those of the bulk plasmon quantum particle. This work opens up for the study of, e.g., squeezed, entangled, and coherent plasmon states in line with what has been studied theoretically and experimentally for photons for many years.

Topological structure of a Nambu monopole in two-Higgs-doublet models: Fiber bundle, Dirac’s quantization, and a dyon

We find a topologically non-trivial structure of the Nambu monopole in two Higgs doublet model (2HDM), which is a magnetic monopole attached by two topologically stable $Z$ strings ($Z$ flux tubes) from two opposite sides. The structure is in sharp contrast to the topological triviality of the Nambu monopole in the standard model (SM), which is attached by a single non-topological $Z$ string. It is found that the Nambu monopole in 2HDM possesses the same fiber bundle structure with those of the `t Hooft-Polyakov monopole and the Wu-Yang description of the Dirac monopole, as a result of the fact that the electromagnetic gauge field is well-defined even inside the strings and is non-trivially fibered around the monopole, while the Nambu monopole in the SM is topologically trivial because electroweak gauge symmetry is restored at the core of the string. Consequently, the Nambu monopole in 2HDM can be regarded as an embedding of the 't Hooft-Polyakov monopole into the $SU(2)_W$ gauge symmetry, and the Dirac's quantization condition always holds, which is absent for the Nambu monopole in the SM. Furthermore, we construct a dyon configuration attached with the two strings.

Torsion driven inflationary magnetogenesis

We show that the breaking of the conformal invariance of the electromagnetic Lagrangian, which is required for inflationary magnetogenesis, arises naturally in the Poincar\'e gauge theory. We use the minimal coupling prescription to introduce the electromagnetic gauge fields as well as non-Abelian gauge fields in this theory. Due to the addition of non-Abelian gauge fields, we show that the solar constraints on this model can be naturally evaded. We find that in the minimal version of this model the generated magnetic field is too small to explain the observations. We discuss some generalizations of the gravitational action, including the Starobinsky model and a model with conformal invariance. We show that such generalizations naturally generate the kinetic energy terms required for magnetogenesis. We propose a generalization of the minimal model by adding a potential term, which is allowed within the framework of this model, and show that it leads to sufficiently large magnetic fields.

Emergent vortex–electron interaction from dualization

We consider the Abelian Higgs model in 3+1 dimensions with vortex lines, into which charged fermions are introduced. This could be viewed as a model of a type-II superconductor with unpaired electrons (or holes), analogous to the boson–fermion model of high-Tc superconductors but one in which the bosons and fermions interact only through the electromagnetic gauge field. We investigate the dual formulation of this model, which is in terms of a massive antisymmetric tensor gauge field Bμν mediating the interaction of the vortex lines. This field couples to the fermions through a nonlocal spin-gauge interaction term. We then calculate the quantum correction due to the fermions at one loop and show that due to the presence of this new nonlocal term a topological B∧F interaction is induced in the effective action, leading to an increase in the mass of both the photon and the tensor gauge field. Additionally, we find a Coulomb potential between the electrons, but with a large dielectric constant generated by the one-loop effects.

Transverse thermopower in Dirac and Weyl semimetals

Dirac semimetals (DSM) and Weyl semimetal (WSM) fall under the generic class of three-dimensional solids, which follow relativistic energy-momentum relation $\epsilon_\mathbf{k}= \hbar v_F |\mathbf{k}|$ at low energies. Such a linear dispersion when regularized on a lattice can lead to remarkable properties such as the anomalous Hall effect, presence of Fermi surface arcs, positive longitudinal magnetoconductance, and dynamic chiral magnetic effect. The last two properties arise due to the manifestation of chiral anomaly in these semimetals, which refers to the non-conservation of chiral charge in the presence of electromagnetic gauge fields. Here, we propose the planar Nernst effect, or transverse thermopower, as another consequence of chiral anomaly, which should occur in both Dirac and Weyl semimetals. We analytically calculate the planar Nernst coefficient for DSMs (type-I and type-II) and also WSMs (type-I and type-II), using a quasi-classical Boltzmann formalism. The planar Nernst effect manifests in a configuration when the applied temperature gradient, magnetic field, and the measured voltage are all co-planar, and is of distinct origin when compared to the anomalous and conventional Nernst effects. Our findings, specifically a 3D map of the planar Nernst coefficient in type-I Dirac semimetals (Na$_3$Bi, Cd$_3$As$_2$ etc) and type-II DSM (PdTe$_2$, VAI3 etc), can be verified experimentally by an in-situ 3D double-axis rotation extracting the full $4\pi$ solid angular dependence of the Nernst coefficient.

Weak-U(1) × strong-U(1) effective gauge field theories and electron-monopole scattering

We present a gauge and Lorentz invariant model for the scattering of matter off magnetic poles, which justifies the presence of velocity-dependent magnetic charges as an effective description of either the behaviour of monopoles in scattering with matter or their production from matter particles at colliders. Hence, in such an approach, perturbativity of the magnetic charge is ensured for relative low velocities of monopoles with respect to matter particles. The model employs a ${\rm U(1)}_{\rm weak} \times {\rm U(1)}_{\rm strong}$ effective gauge field theory under which electrons and monopoles (assumed to be fermions) are appropriately charged. The non-perturbative quantum effects of the strongly coupled sector of the theory lead to dressed effective couplings of the monopole/dyon with the electromagnetic photon, due to non-trivial wave-function renormalization effects. For slowly-moving monopole/dyons, such effects lead to weak coupling, thus turning the bare non-perturbative magnetic charge, which is large due to the Dirac/Schwinger quantization rule, into a perturbative effective, velocity-("$\beta$")-dependent magnetic coupling. Our work thus offers formal support to previous conjectural studies, employing effective U(1)-electromagnetic gauge field theories for the description of monopole production from Standard Model matter, which are used in contemporary collider searches of such objects. This work necessarily pertains to composite monopoles, as seems to be the case of all known monopoles so far, that are solutions of specific particle physics models. This is a consequence of the fact that the wave-function renormalization of the (slowly-moving) monopole fermion turns out to violate unitarity bounds that would characterise asymptotic elementary particle states.

Spinning particle interacting with electromagnetic and antisymmetric gauge fields in anti-de Sitter space

Massless spinning particle model that interacts with electromagnetic and antisymmetric gauge fields in anti-de Sitter space-time is considered as a constrained Hamiltonian system. d-dimensional anti-de Sitter space-time is realized as a real projective manifold parametrized by the homogeneous coordinates. Classical constraints that generate in the presence of interactions minimal world-line supersymmetry algebra extended by the dilatations of the ambient-space homogeneous coordinates are found. Various representations of the Lagrangian of the spinning particle are obtained. Dirac quantization is shown to produce first- and second-order equations for the wave function of the spinning particle that are presented in the homogeneous, inhomogeneous and intrinsic coordinates of AdS_d.

Toward electrodynamics of unconventional phases of dilute nuclear matter

The phase diagram of isospin-asymmetrical nuclear matter may feature a number of unconventional phases, which include the translationally and rotationally symmetric, but isospin-asymmetrical BCS condensate, the current-carrying Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase, and the heterogeneous phase-separated phase. Because the Cooper pairs of the condensate carry a single unit of charge, these phases are charged superconductors and respond to electromagnetic gauge fields by either forming domains (type-I superconductivity) or quantum vortices (type-II superconductivity). We evaluate the Ginzburg-Landau (GL) parameter across the phase diagram and find that the unconventional phases of isospin-asymmetrical nuclear matter are good type-II superconductors and should form Abrikosov vortices with twice the quantum of magnetic flux. We also find that the LOFF phase at the boundary of the transition to the type-I state, with the GL parameter being close to the critical value .

Interpolating Quantum Electrodynamics

We discuss the interpolation between the instant form dynamics (IFD) and the light-front dynamics (LFD) proposed by Dirac in 1949 and present its application to quantum electrodynamics (QED). Our analysis clarifies any conceivable confusion in the prevailing notion of the equivalence between the IFD at infinite momentum frame and the LFD. Entwining the fermion propagator interpolation with our previous works of the interpolating helicity spinors and the electromagnetic gauge field interpolation, we fasten the bolts and nuts necessary to launch the interpolating QED at least in the tree level.

Hadronic Lorentz violation in chiral perturbation theory including the coupling to external fields

If any violation of Lorentz symmetry exists in the hadron sector, its ultimate origins must lie at the quark level. We continue the analysis of how the theories at these two levels are connected, using chiral perturbation theory. Considering a two-flavor quark theory, with dimension-4 operators that break Lorentz symmetry, we derive a low-energy theory of pions and nucleons that is invariant under local chiral transformations and includes the coupling to external fields. The pure meson and baryon sectors, as well as the couplings between them and the couplings to external electromagnetic and weak gauge fields, contain forms of Lorentz violation which depend on linear combinations of quark-level coefficients. In particular, at leading order the electromagnetic couplings depend on the very same combinations as appear in the free particle propagators. This means that observations of electromagnetic processes involving hadrons--such as vacuum Cerenkov radiation, which may be allowed in Lorentz-violating theories--can only reliably constrain certain particular combinations of quark coefficients.

Hilbert series and operator basis for NRQED and NRQCD/HQET

We use a Hilbert series to construct an operator basis in the 1/m expansion of a theory with a nonrelativistic heavy fermion in an electromagnetic (NRQED) or color gauge field (NRQCD/HQET). We present a list of effective operators with mass dimension d≤8. Comparing to the current literature, our results for NRQED agree for d≤8, but there are some discrepancies in NRQCD/HQET at d=7 and 8.